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Express in terms of sine and cosine Calculator

Get detailed solutions to your math problems with our Express in terms of sine and cosine step-by-step calculator. Practice your math skills and learn step by step with our math solver. Check out all of our online calculators here!

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1

Solved example of express in terms of sine and cosine

$\frac{1-\tan\left(x\right)}{1+\tan\left(x\right)}$
2

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\frac{1+\frac{-\sin\left(x\right)}{\cos\left(x\right)}}{1+\tan\left(x\right)}$
3

Applying the tangent identity: $\displaystyle\tan\left(\theta\right)=\frac{\sin\left(\theta\right)}{\cos\left(\theta\right)}$

$\frac{1+\frac{-\sin\left(x\right)}{\cos\left(x\right)}}{1+\frac{\sin\left(x\right)}{\cos\left(x\right)}}$
4

Combine all terms into a single fraction with common denominator

$\frac{\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}}{1+\frac{\sin\left(x\right)}{\cos\left(x\right)}}$
5

Combine all terms into a single fraction with common denominator

$\frac{\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)}}{\frac{\cos\left(x\right)+\sin\left(x\right)}{\cos\left(x\right)}}$
6

Simplify the fraction

$\frac{\left(\cos\left(x\right)-\sin\left(x\right)\right)\cos\left(x\right)}{\cos\left(x\right)\left(\cos\left(x\right)+\sin\left(x\right)\right)}$
7

Simplify the fraction $\frac{\left(\cos\left(x\right)-\sin\left(x\right)\right)\cos\left(x\right)}{\cos\left(x\right)\left(\cos\left(x\right)+\sin\left(x\right)\right)}$ by $\cos\left(x\right)$

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)+\sin\left(x\right)}$

Final Answer

$\frac{\cos\left(x\right)-\sin\left(x\right)}{\cos\left(x\right)+\sin\left(x\right)}$

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